Please use the coordinates given in the figure to draw the free-body diagram for
ID: 1434200 • Letter: P
Question
Please use the coordinates given in the figure to draw the free-body diagram for the crate. Then write down Newton's second law for each coordinate direction for the crate of mass m that slides down the incline of angle 6 with kinetic friction between the crate and incline. That is, write summation F_x = ma_x and summation F_y =ma_y in detail for this particular problem. The coefficient of kinetic friction is mu_k. Solve the equations for a_x, the acceleration in the X-direction. The final answer should be in terms of 6, g, mu_k ONLY.Explanation / Answer
Forces balance along y axis : mgcos(theta) = N
Force balance along x axis : mgsin(theta) - f = ma
but, f = mu N
so, mgsin(theta) - mu*mgcos(theta) = ma
a = gsin(theta) - mu*gcos(theta)